Two cases of spatial transformations

Abstract

Here, we give an overview of our work on two topics related to the theme of spatial transformations in wave theory, namely the concepts of transformation electronics and 'digital' metamaterials. In the first topic, we show that the notion of transformation optics can be extended to other physical phenomena such as tailoring the effective mass of charged carriers, e.g. electrons, in specially designed semiconductor superlattices. We discuss how the combination of thin layers of electronic materials with different effective mass of electrons may lead to bulk composite structures in which the effective mass of electrons may exhibit extreme anisotropy. For the second case, we show that any desired electromagnetic permittivity can, in principle, be engineered with proper combinations of two deeply subwavelength building blocks with relative permittivity values whose real parts have opposite signs. Owing to the presence of a plasmonic resonance between the two building blocks with oppositely signed dielectric constants, the achieved effective relative permittivity for the bulk composite may have values outside the range defined by the two permittivity values of the building blocks. We discuss some of the salient features of these two spatial transformation phenomena.

Spatial transformations: from fundamentals to applications

“…The brief review we have given in §1, combined with the papers in this themed issue, demonstrate the wealth of potential in the spatial transformations approach, from the relatively well established transformation optics to new proposals for 'transformation electronics' [17], such that it is now possible to speak of 'transformation physics'. The basic approach of spatial transformations has been described, together with numerous advanced techniques, such as complex coordinate transformations [14], and advanced applications, such as manipulation of optical forces [16].…”

“…This emphasizes the close links between the fields of spatial transformations and metamaterials and also nano-composite materials. The papers from Silveirinha et al [17], Rumpf et al [13] and Grant et al [18] all contribute different perspectives on the fabrication of materials for transformation electromagnetics.…”

“…The resulting effective mass of the semiconductor superlattice can have extremely anisotropic behaviour, including effective masses near zero and extremely high positive values. The resulting potential enhancements in conductivity are described, with extensions to graphene electronics noted, among other possible applications of the spatial transformations paradigm [17].…”

“…In the remainder of that paper, the authors turn to methods for implementing spatial transformation designs, with a discussion of the 'digital metamaterials' concept [17]. In this approach to realizing metamaterials with the required properties, an analogy is drawn between how digital bytes are made from bits on the one hand, and the use of two different metamaterial 'bits' (a 'one' and a 'zero') to achieve a metamaterial 'byte' with properties formed from the average of the bits.…”

“…The first topic continues the discussion of advanced applications of spatial transformations by describing their work on 'transformation electronics', which is the application of spatial transformations and metamaterials to semiconductor electronics [17]. They begin with an exploration of the possibility of applying spatial transformation concepts to the effective mass of an electron and suggest three examples to show why this concept is of interest [17]. First, engineering the effective mass of electrons may improve speed and response times in electronic and optical systems, by increasing mobility and conductivity.…”